Question

以知∠AOC=150°,OB是∠AOB的平分线，OF,OE分别是∠AOB和∠BOC的平分线，求∠EOF的度数。

以知∠AOC=150°,OB是∠AOB的平分线，OF,OE分别是∠AOB和∠BOC的平分线，求∠EOF的度数。

Answer 1

先纠个小错：OB是∠AOC的平分线，不可能是∠AOB的平分线。

∠EOF = ∠EOB + ∠FOB
= ∠AOB/2 + ∠COB/2
= (∠AOB + ∠COB)/2
= ∠AOC/2
= 150°/2
= 75°

Answer 2

解：(1)设∠BOE = α ∠AOD= β ∠AOE=δ ∠DOE=θ
∵∠AOC为锐角,OD平分∠AOC,OE平分∠BOC.
∴∠BOE =∠EOC= α ∠AOD=∠DOC= β
又∵∠EOC= ∠AOD + ∠DOC + ∠AOE = 2β + δ = α
∴ ∠AOB= 90° = ∠BOE+∠AOE = α + δ = 2β + 2δ
∴ ∠DOE= θ = β + δ = 1/2 ∠AOB = 45°
(2) 当∠AOB=m°时, ∠DOE= θ = β + δ = 1/2 ∠AOB = m°/2